THE CORRECTING FUNCTIONS METHOD FOR SOLVING A BOUNDARY VALUE PROBLEM FOR THE AMBIPOLAR DIFFUSION EQUATION IN A DOMAIN WITH A CURVILINEAR BOUNDARIES
An approach for the ambipolar diffusion equation boundary value problem solving, which is posed in a two-dimensional domain with oscillating boundaries, is proposed. The construction of the solution of the model problem is based on the corresponding problem for a certain internal canonical majorant domain and the methodology for constructing the so-called corrective corrections based on the use of the perturbation theory elements. A feature of this problem is that it is not the problem equation or boundary conditions that are perturbed, but the region. And this leads to the construction of a fundamentally new solution structure.
Sze S., Kwok K. Physics of Semiconductor Devices. New York: Wiley-Interscience, 2006. 815 p.
Bomba A. Ya., Gladka O. M. Synthesis of numerical methods of quasicondormal mappings, summary mapping and domain decomposition for solving nonlinear boundary problems in layered media. Journal of Numerical and Applied Mathematics, 2012. No 2 (108). P. 20–31.
Fuchs B. A. Shabat B. V. Functions of a complex variable and some of their applications. Pergamon Press, 1964. 458 p.
Bomba A., Moroz I., Boichura M. The optimization of the shape and size of the injection contacts of the integrated p-i-n-structures on the base of using the conformal mapping method. Radio Electronics, Computer Science, Control. 2021. No 1. P. 14–27.
Lyashko I. I., Velikoivanenko I. M., Lavryk V. I., Mistetskyi G. E. Method of majorant domains in filtration theory. Kiev: Naukova Dumka, 1974. 200 p.
Kobler W., Papanicolaou G., Varadhan S. Boundary and Interface Problems in Regions with Very Rough Boundaries. In Multiple Scattering and Waves in Random Media. Eds. Chow P. L., Kohier W. E., Papanicolaou G. C. Amsterdam: North-Holland Publishing Co., 1981. P. 165–197.
Vasil’eva A. B., Butusov V. F. Kalachev L. V. The Boundary Function Method for Singular Perturbation Problems. SIAM: Philadelphia, 1995. 257 p.
Bomba A., Moroz, I., Boichura M. Development and analysis of a mathematical model of plasma characteristics in the active region of integrated P-I-N-structures by the methods of perturbation theory and conformal mappings. Eastern European Journal of advanced technologies. 2021. No 5 (113). P. 51–61.